Antennas having more than one set of windings are described in the prior at.
GB-279,935 describes an antenna unit for use in wireless telecommunication, the unit comprising two frame windings having different natural wavelengths and arranged so that there is substantially no interaction between the said windings.
U.S. Pat. No. 7,123,206 describes a system comprising multiple antennas wound around a common core, adapted for use in an inductively coupled system for transmitting or receiving electromagnetic signals in three dimensions.
DE 195 33 105 describes an antenna unit for a car comprising three coils, which are perpendicular to each other and adapted for receiving horizontally as well as vertically polarized signals (e.g. TV and radio signals, respectively).